Molecular motors are multicomponent molecular structures that consume energy to induce motion and to generate forces. Their dynamics covers various time and length scales and critically depends on chemical-mechanical coupling, external forces and molecular properties such as diffusion, particle distribution and density. The complex behavior of these systems consequently offers a formidable challenge for theoretical descriptions and numerical approaches that aim to provide a computational laboratory for a fundamental analysis of the underlying interaction mechanisms as well as interpretations or to study control of the system's behavior. Coupling a linear molecular motor system to an energy supply can induce movement of the motor molecules along a filamentous structure. The complex dynamics of bound (i.e. attached to a filament) and free (i.e. diffusing in the surrounding medium) molecular motors thereby may depend on the diffusive properties of the molecules and on the excitation process driving the motor system. Our theory is therefore based on spatially dependent Fokker-Planck equations for the dynamics of bound and free motors. The model considers spatially inhomogeneous transition rates coupling the energetic sublebels of the molecules as well as spatial fluctuations and diffusion. Computational modelling of the spatio-temporal dynamics of molecular motors shows that both, molecular diffusion and bandwidth of the transition rate set an upper limit to the efficiency of the motor progression. A sufficiently small molecular diffusion as well as a thorough adjustment of transition rates lead to a regular forward propagation while for high diffusion and improperly chosen rates spatio-temporally diverging particle distributions may evolve. Suitable excitation conditions for efficient movement-control are discussed.
The dynamics of ultrashort pulses propagating in a quantum dot amplifier is determined by a complex nonlinear coupling and dynamic interplay of light fields and carriers in the spatially inhomogeneous quantum dot ensemble. Computational modeling shows that in spite of the large complexity the strong localization of the carrier inversion and the low amplitude phase coupling may allow the amplification and transmission of ultrahort light pulses with minimum deterioration of the pulse properties (e.g. pulse shape, duration). The theoretical description is based on spatially resolved Quantum Dot Maxwell-Bloch equations that describe the spatio-temporal light field and inter-/intra-level carrier dynamics in each quantum dot of a typical quantum dot ensemble. In particular, this includes spontaneous luminescence, counterpropagation of amplified spontaneous emission and induced recombination as well as carrier diffusion in the wetting layer of the laser. Intradot scattering via emission and absorption of phonons, as well as the scattering with the carriers and phonons of the surrounding wetting layer are dynamically included on a mesoscopic level. Spatial fluctuations in size and energy levels of the quantum dots and irregularities in the spatial distribution of the quantum dots in the active layer are simulated via statistical methods. Simulation results of the nonlinear pulse propagation in quantum dot optical amplifiers allow visualization and interpretation of fundamental nonlinear processes such as selective depletion and re-filling of quantum dot energy levels leading to a complex gain and index dynamics that affect the amplitude and phase of a propagating light pulse. Computational modelling thus may lay the foundation for an optimization and tayloring of pulse properties.
The high-speed modulation dynamics of semiconductor lasers is determined by a complex interplay of ultrafast carrier and light field dynamics. The characteristic time scales of the underlying physical processes determine the relaxation oscillations and set an upper limit to the modulation of a single-mode semiconductor laser. In spatially extended semiconductor lasers the longitudinal and transverse dimensions enable the coexistence of numerous longitudinal and transverse modes. A suitable design of the laser cavity and electronic contacts should consequently allow one to directly influence the lateral coupling and transverse mode dynamics. The twin-stripe semiconductor laser (realized with two parallel contacts on top of the active area) represents one of the simplest semiconductor lasers with coexisting transverse modes. Modulation of the current in the stripes with a beat frequency corresponding to the frequency separation of transverse modes may then lead to a significant increase of the high-frequency modulation response of the laser. In this paper, we present results of simulations on the modulation characteristics of twin-stripe semiconductor lasers on the basis of multi-mode Maxwell Bloch equations that include propagation effects and spatio-temporally varying mode competition. In particular, we analyze the dependence of light field dynamics and spectral properties on laser dimensions, carrier injection and modulation frequency. Our simulations reveal that it is both, the transverse and the longitudinal degree of freedom that influence the transverse mode dynamics as well as the laser response to high-frequency modulation.
The quantum dot laser is a complex nonlinear system in which light fields dynamically interact with the charge carriers in the dots and the embedding quantum well medium. In real laser systems, typical dot-to-dot variations in size, energy levels and material parameters exist. In addition, the dots are not equally positioned on a grid within the layers. The respective variance in quantum dot parameters and dot-to-dot distance depends on the material system and the epitaxial growth process of the particular quantum dot system. To elucidate the influence of spatial fluctuations, we calculate the temporal light field dynamics of quantum dot lasers with variable fluctuations in the characteristic dot parameters. The simulations on the coupled ultrafast spatio-temporal light-field and carrier dynamics in quantum dot lasers are based on a two-level Multi-Mode Maxwell-Bloch description. The constituent equations consist of coupled spatio-temporally resolved wave equations and Bloch equations for the carriers within each quantum dot of a dot ensemble constituting the active gain medium of a quantum dot laser. It is shown that the light field dynamics and the emission spectra are strongly determined by the nonlinear coupling between the light fields and the charge carrier plasma, spatially varying material properties of the quantum dot ensemble as well as device geometry and carrier injection.